Oxidizing an alcohol is fundamentally about removing a C-H bond from the carbon bearing the hydroxyl group and replacing it with a new C=O bond. This immediately explains why alcohol class matters so much to the outcome: a primary alcohol has two C-H bonds on its hydroxyl-bearing carbon, so it can be oxidized once (to an aldehyde) and, if conditions allow, a second time (all the way to a carboxylic acid). A secondary alcohol has only one C-H bond on that carbon, so it can be oxidized exactly once, stopping at a ketone with nowhere further to go. A tertiary alcohol has zero C-H bonds on its hydroxyl-bearing carbon — there's simply nothing left to remove, so tertiary alcohols cannot be oxidized by these reagents at all.

This C-H-counting logic explains the substrate side of the reaction completely, but for primary alcohols specifically, there's still a real choice to make: do you want to stop at the aldehyde, or push all the way through to the carboxylic acid? That choice is entirely a function of which oxidizing agent you select.

Putting the substrate-side and reagent-side logic together gives a complete picture worth holding in your head as a single reference: a primary alcohol oxidized with PCC gives an aldehyde and stops there; the same primary alcohol oxidized with KMnO₄ or K₂Cr₂O₇ continues through to a carboxylic acid. A secondary alcohol gives a ketone with any of these oxidants — there's no further oxidation possible regardless of which reagent is chosen, since a ketone has no hydrogen left on its carbonyl carbon. A tertiary alcohol is untouched by any of these oxidants, full stop.

This reagent-choice distinction is one of the most practically important pieces of alcohol chemistry in synthesis planning: if a chemist specifically needs an aldehyde as an isolable product (rather than having it oxidize further), PCC is the deliberate choice; if a carboxylic acid is the actual target, a stronger aqueous oxidant is chosen instead.